What is Google pagerank?
Google developed the "pagerank" system several years ago for the purpose of gauging how "important" a web page is. The higher the pagerank, the more "important" Google thinks the webpage is. Google uses this gauge as a part of its ranking algorithm.
Where does pagerank come from?
Pagerank is all about webpages linking to other webpages. You see, every page that Google indexes has a pagerank value associated with it. Every time one page links to another page, a portion of that pagerank value "passes" to the page it links to. Higher ranking pages, pass more pagerank to the pages they link to.
What happens is, when one page links to another page, it's kind of like the page that does the linking is voting for the other page. So to get pagerank to your webpage, all you have to do is get other pages to link to it.
Pagerank is really just a mathematical calculation that determines how "important" a webpage is based on how "important" the pages that link to it are.
A crucial point here that is often misunderstood is that pagerank is passed on a page by page basis. Many webmasters assume that a sites pagerank is determined by its home page. While it's true that the homepage is often the highest ranking page within a website, it doesn't have to be. Any page on a given website could rank higher then the homepage.
The myth that the homepage will have the highest pagerank comes from the fact that many webmasters (especially old school webmasters) participated in reciprocal linking programs where they would exchange links to each others homepages. So, by default, the homepage wound up with the highest pagerank simply because it had the most links pointing to it.
So how will my pagerank affect my search engine rankings?
Pagerank is simply not as powerful as it once was. There was a time when all you had to do to rank well was to get enough websites to link to you and you could dominate virtually any listing you wanted. Today, the ranking algorithm is much more complex. Many other factors are taken into account. However, pagerank does still play a reasonably important roll so getting backlinks is still a major task in the search engine optimization world. It's just that the way we go about getting those links has changed.
How do I check a sites pagerank?
Google offers a free toolbar that you can download and install on your machine. One of the things this toolbar does is to display the Pagerank of whatever webpage you're looking at.
One final note, my recommendation is to never worry too much about Pagerank. Build your website to the best of your ability; create well written, compelling web pages and you'll get backlinks naturally. Further, take some of your better articles and submit them to a few article directories - include a resource box which links back to your site and you'll get some excellent backlinks pretty quickly. Just stay away from reciprocal linking campaigns, whatever benefit they once had is long gone.